Happy Pi Day

For Pi day today we explored the amazing near integer e^{ \pi \sqrt{163}}

I started by showing the boys the numbers as well as just how close it was to being an integer. I measured the closeness both in terms of the decimal expansion and in terms of the continued fraction expansion of the number:

Next I asked the boys to each take a turn finding another number relating to \pi that was either nearly an integer or nearly a rational number. It turned out – especially with my younger son – to be a really nice way to discuss properties of powers of numbers.

The number my younger son found was 100 * 314^{\pi}

The number my older son found was 3.4 * \pi^{\sqrt{2}}

So – obviously just for fun – but still a neat way to talk about numbers and continued fractions. And a pretty fun number at the start, too 🙂

A review of “The Sherlock”

We received a nice gift from Jim Propp earlier this month. With the kids off of school for a snow day today, it seemed like a good time to open it up.

My younger son played with it for a while and then I wanted to have him show how the game worked. Here are his initial thoughts about the game:

Here’s the first example of a puzzle solve. You’ll see that even having solved it once before it is still not necessarily so simple:

Here’s a second solve example – this one goes pretty quickly

Finally, we wrapped up by having him show some of the other pieces and me asking him to talk about what he thinks the main ideas are for this puzzle. Interestingly he doesn’t think that it is a math puzzle, but rather a logic puzzle 🙂

So, thanks to Jim Propp for giving us this really nice puzzle game.